How can I transfer music between iPod and my iPhone 13?

You cannot move them directly.

Music on an iPod Classic was added from your iTunes Library and it should still be there. To add that music to your iPhone, you the iTunes Library that contains the music. If you are on a Mac, with the newer operating system that does not use iTunes, use the Mac's Finder instead.

If you no longer have your old iTunes Library, then either:

• use a third-party programme to copy the music from the iPod Classic back onto your computer and then copy that to the phone
• re-build your library by going back to your original source of the music:
  • music form CDs - copy from the CD again
  • music purchased from online stores - go to your account with that store and re-download the songs